1. Field of Invention
The present invention relates to a method of sub-sampling interpolation, and particularly relates to a method of sub-sampling interpolation for performing sub-sampling transmission of a picture signal.
2. Background Art
In a known system for compressing the band width required to transmit a picture signal, a sub-sampling transmission system produces sampled values obtained through sub-sampling effected in each of a plurality of successive periods, each having a predetermined length which is N times as long as a period of one picture signal field (N being a natural number). These sampled values are successively transmitted. The transmitted sampled values in each of the periods of predetermined length are used to interpolate non-transmitted sample values in the period of predetermined length to thereby reproduce an original picture signal. There are various forms of sampling transmission systems. Two well known forms are the field offset sub-sampling technique and the line offset sub-sampling technique.
Where sampling points are arranged in a square lattice, as shown in FIG. 8, when a picture signal is sampled, the spatial freqency range which can be transmitted being as shown in FIG. 9, a sampling interval is represented by .DELTA.x and a scanning line interval is represented by .DELTA.y. FIGS. 10 and 12 show sampling patterns, respectively, for performing the field offset sub-sampling and the line offset sub-sampling on a picture signal which has been subjected to sampling on the basis of the sampling pattern of FIG. 8. In each of FIGS. 10 and 12, the positional relationship of sampling points in two successive fields is shown. In the positional relationship of sampling positions illustrated in the drawings, sampled values at sampled points represented by the mark of O and aligned on solid lines are transmitted in the n-th field (n being a natural number), and sampled values at sampling points represented by the mark of O and aligned on broken lines are transmitted in the (n+1)-th field. The mark x designates sampling points which are not transmitted.
The ranges which can be transmitted for the field offset sampling technique and for the line offset sampling technique are as shown in FIGS. 11 and 13, respectively.
If it is assumed that the range to be transmitted by the offset sub-sampling technique is composed of zones A, B and C, illustrated in FIG. 14, the respective components of zones A, B and C are reflected so as to generate zones A', B' and C' by the sub-sampling carrier when the offset sub-sampling is made with respect to a signal band-limited to the zones A, B and C. Consequently, an actually transmitted signal has a spectrum extending over a range consisting of the zones A, B, C, A', B', and C'. Therefore, in order to eliminate unnecessary components caused by reflection of the sub-sampling carrier, it is necessary to provide a pre-filter for limiting the band into a transmissible range at the transmitter sides. At the same time, it is necessary to provide a post-filter having LPF (low pass filter) arrangement at the receiver side so as to pass the signal through the LPF arrangement to thereby eliminate the components of the zones A', B' and C' before interpolation of the non-transmitted points is carried out.
In such a conventional method of sub-sampling interpolation, in which the interpolation of non-transmitted points is performed at the receiver side, a two-dimensional digital filter has been used as a post-filter.
If the two-dimensional digital filter acting as a post-filter is a FIR (finite impulse response) filter, tap coefficients of the two-dimensional digital filter can be obtained as shown in FIG. 15 on the basis of inverse-DFT (discrete Fourier transformation). In FIG. 15, numerals at the left side represent the number of the taps constituting the filter.
If each of the tap coefficients is multiplied by a Hamming window so as to make the tap length finite, the characteristics of a 3.times.3 tap filter and a 11.times.11 tap filter can be obtained on the basis of a DFT, as shown in FIGS. 16 and 17, respectively. As shown in FIGS. 16 and 17, a triangular passing range can be satisfied when the number of taps in a filter is 11.times.11 or more.
The actual sub-sampling transmission of a picture signal was simulated on a computer, the result of simulation being shown in FIGS. 18 to 20. The FIG. 18 diagrams each shows sampled values obtained at respective sampling points by sampling an original picture signal having components arranged only in the horizontal scanning direction, where the sampling frequency is selected to 48 MHz and the sampling points are arranged in a square lattice. In diagrams (A) to (E) of FIG. 18, the sampled values at the respective sampling points are shown for picture signal frequencies set to 20 MHz, 16 MHz, 12 MHz, 8 MHz and 4 MHz, respectively, under the conditions that, in each case, the picture signal consists only of components in the horizontal scanning direction and the magnitude of the sampled value at each sampling point is represented by the magnitude of the diameter of the mark O. The signal obtained by such sampling is passed through a pre-filter, which may be a two-dimensional filter having taps the number of which is 11.times.11, and then subjected to sampling so as to obtain sampled values. The thus obtained sampled values are transmitted, and the transmitted sampled values are received and then subjected to interpolation through a two-dimensional filter having taps the number of which is 3.times.3 to thereby obtain such sampled values as shown in the respective diagrams (A) to (E) of FIG. 19. Alternatively, if the transmitted and received sampled values are subjected to interpolation through a two-dimensional filter having taps the number of which is 11x11, sampled values as shown in the respective diagrams (A) to (E) of FIG. 20 are obtained. However, the 3.times.3 tap filter used to obtain the results illustrated in FIG. 19 is not the same as that of FIG. 16, but has coefficients arranged to make the band extend horizontally as well as vertically. The coefficients of this 3.times.3 tap filter are shown in FIG. 21.
From this simulation, it is found that components not lower than 16 MHz can not be reproduced when a 3.times.3 tap filter is used as a post-filter, and components of 20 MHz can not be effectively reproduced even when a 11.times.11 tap filter is used.
Accordingly, in the conventional method of sub-sampling interpolation, wherein the interpolation is performed by using a two-dimensional filter, there exists the problem that the transmission band is reduced which thereby lowers the resolution of a reproduced picture, unless a larger two-dimensional filter having taps the number of which is not smaller than 11.times.11 is used. Therefore, it is necessary to provide such a larger two-dimensional filter and the circuit arrangement at the receiver is necessarily of large size.